软代数的理想和同余关系  

IDEALS AND CONGRUENCES OF SOLF ALGEBRAS

作　　者：郑延履[1] 

机构地区：[1]武汉大学数学系

出　　处：《模糊系统与数学》1994年第2期77-82,共6页Fuzzy Systems and Mathematics

摘　　要：本文刻划了使软代数Ｆ的任意二元ａ，ｂ在一个同余类的最小同余关系（定理１），Ｆ的理想可以成为某个同余关系的核的充分必要条件（定理２），以Ｆ的同余理想Ｉ为核的最小和最大的同余关系（定理３）．The main results in this paper are as follows:Theorem 1 Let F be a solf algebra,a,b∈F,a≤b, Then relations Q_1 and Q_2 when x∧a=y∧a,x∨b=y∨b,when x'∧a=y'∧a,x'∨b=y'∨b。are congruence relations on F as lattice,Again,Q_1∨Q_2 is a minimal congruence relationfor on F as solf algebra. Theorem2 The ideal I=(d]of a solf algebra F is kernel of a congruence relation ifand only if d=d':d∧d',where d':d∧d'is the relative pseudo-complement of d'ind∧d'.Theorem 3 Let I=(d]be a congruence ideal of a solf algebra F Then the relation(I) when i)If y then. is a maximal congruence relation with kernel I on F.

关 键 词：软代数 同余关系 理想 同余理想 

分 类 号：O153.2[理学—数学]